Jamming and percolation of k2-mers on simple cubic lattices

Abstract

Geometric phase transition of cubes and tiles (k×k×k and k×k>×1) deposited on simple cubic lattices have been studied by numerical simulations complemented with finite-size scaling theory. The objects were irreversibly deposited into the lattice. The Jamming coverage θj was determined over a wide range of values of k, showing a monotonic decreasing behaviour with the object size. In addition, a finite-size scaling analysis of the jamming transition was carried out and the corresponding spatial correlation length critical exponent νj was measured for both species. On the one hand, the results for the percolation threshold of cubes, θc,k, showed an increasing dependence with k in the range 2 < k < 16. For k > 17, all jammed configurations are non-percolating states, and consequently, the percolation phase transition disappears. In the case of tiles, the obtained results for the percolation threshold showed a non-monotonic dependence with the object size, being a decreasing function of k in the range 2 < k < 14, reaching a minimum at k = 15, and finally increasing for k > 16. Finally, a complete analysis of critical exponents and universality have been done, showing that the percolation phase transition involved in the system has the same universality class as the 3D random percolation regardless of the object considered.